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mart [117]
3 years ago
15

Find the equation of a parabola with a vertical axis and its vertex at the origin and passing through the point (-2, 3).

Mathematics
1 answer:
jonny [76]3 years ago
5 0

Answer:

y=\frac{3}{4}x^2

Step-by-step explanation:

Hi there!

Because we're given the vertex of the parabola, we can determine its equation in vertex form:

y=a(x-h)^2+k where the vertex is (h,k)

Plug in the vertex (0,0)

y=a(x-0)^2+0\\y=a(x)^2\\y=a(x-0)^2+0\\y=ax^2

Now, we must solve for a. Plug in the given point (-2,3) and solve for a:

3=a(-2)^2\\3=4a\\\frac{3}{4} =a

Therefore, the value of a is \frac{3}{4}. Plug this back into y=ax^2:

y=\frac{3}{4}x^2

I hope this helps!

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